By Wolfgang Fellin (auth.), a.o. Univ.-Prof. Dipl.-Ing. Dr. Wolfgang Fellin, em. Univ.-Prof. Dipl.-Ing. Heimo Lessmann, a.o. Univ.-Prof. Dr. Michael Oberguggenberger, Dipl.-Ing. Robert Vieider (eds.)
This quantity addresses the difficulty of uncertainty in civil engineering from layout to building. mess ups do happen in perform. Attributing them to a residual process hazard or a defective execution of the venture doesn't correctly disguise the variety of explanations. a better scrutiny of the followed layout, the engineering version, the knowledge, the soil-construction-interaction and the version assumptions is needed. frequently, the uncertainties in preliminary and boundary stipulations are ample. present engineering perform usually leaves those concerns apart, although new clinical instruments were constructed some time past many years that permit a rational description of uncertainties of all types, from version uncertainty to information uncertainty. it's the goal of this quantity to have a severe examine present engineering danger thoughts so that it will bring up expertise of uncertainty in numerical computations, shortcomings of a strictly probabilistic safeguard suggestion, geotechnical versions of failure mechanisms and their implications for development administration, execution, and the juristic query of accountability. additionally, many of the new systems for modelling uncertainty are defined. The ebook is as a result of the a collaborate attempt of mathematicians, engineers and development managers who met on a regular basis in a submit graduate seminar on the college of Innsbruck in past times years.
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Sample text
When fitted to the data of Tab. 1, both distributions, normal and lognormal, pass the standard statistical tests (Kolmogorov-Smirnov and χ2 , see Tab. 3), but as we see in Fig. 1, they do not match the peak of the histogram and its asymmetry very well. A better statistical fit is given by the two following distributions. Lognormal distribution with three parameters: We shift the lognormal distribu2 ). tion by the lower limit of the friction coefficient ν0 : ln(ν−ν0 ) ∼ (µln(ν−ν0 ) , σln(ν−ν 0) The distribution parameters are chosen by maximizing the likelihood function of the given sample (maximum likelihood method).
The probabilistic input in the model consists in specifying the types of probability distributions of the variables under consideration as well as the parameters of the distributions. We first point out that probability plays several roles here. It has to describe as diverse things as • • • • measurement errors, spatial data fluctuations, model deficiencies, lack of information. While measurement errors can be considered as approximately random, there are strong arguments against the presumption of randomness of spatial data fluctuations.
It is devoid of any real-world meaning, and in particular, can never have a rational - verifiable - interpretation as a frequency of failure. It is regrettable that in public statements about safety the different interpretations of probability theory are frequently mixed in an unjustified and possibly misleading way. For a similar, historical discussion of the evolvement of the numerical values of reliability assessments in the aerospace-, nuclear- and chemical process sectors we refer to [8]. Putting these delicate general questions aside (an excellent overview of the different interpretations of probability is [33]), we shall pursue the more modest goal of capturing parameter variability in this article.